Kevin is 32 years older than Daniel. Kevin and Daniel first met 3 years ago. Four years ago, Kevin was 5 times older than Daniel. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and Daniel. Let Kevin's current age be $k$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $k = d + 32$ Four years ago, Kevin was $k - 4$ years old, and Daniel was $d - 4$ years old. The information in the second sentence can be expressed in the following equation: $k - 4 = 5(d - 4)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $d$ and substitute it into our second equation. Solving our first equation for $d$ , we get: $d = k - 32$ . Substituting this into our second equation, we get the equation: $k - 4 = 5($ $(k - 32)$ $ -$ $ 4)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 4 = 5k - 180$ Solving for $k$ , we get: $4 k = 176$ $k = 44$.